A train travelling at a speed of 75 mph enters a tunnel \(3\frac{1}{2}\) miles long. The train is \(\frac{1}{4}\) mile long. How long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?

A. 3 min
B. 4 min
C. 3.7 min
D. 3.2 min

Solution:

\[\left. \begin{array} { l } { \text { Total distance covered } = ( \frac { 7 } { 2 } + \frac { 1 } { 4 } ) \text { miles } } \\ { \qquad = \frac { 15 } { 4 } \text { miles. } } \\ { \therefore \text { Time taken } = ( \frac { 15 } { 4 \times 75 } ) \text { hrs } } \\ { = \frac { 1 } { 20 } \text { hrs } } \\ { = ( \frac { 1 } { 20 } \times 60 ) \text { min. } } \\ { = 3 \text { min. } } \end{array} \right.\]

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